Coordinating tiny limbs and long bodies: Geometric mechanics of lizard terrestrial swimming

Animal-Morphing Bio-Inspired Mechatronic Systems: Research Framework in Robot Design to Enhance Interplanetary Exploration on the Moon

Over the past 50 years, the space race has potentially grown due to the development of sophisticated mechatronic systems. One of the most important is the bio-inspired mobile-planetary robots, actually for which there is no reported one that currently works physically on the Moon. Nonetheless, significant progress has been made to design biomimetic systems based on animal morphology adapted to sand (granular material) to test them in analog planetary environments, such as regolith simulants. Biomimetics and bio-inspired attributes contribute significantly to advancements across various industries by incorporating features from biological organisms, including autonomy, intelligence, adaptability, energy efficiency, self-repair, robustness, lightweight construction, and digging capabilities-all crucial for space systems. This study includes a scoping review, as of July 2024, focused on the design of animal-inspired robotic hardware for planetary exploration, supported by a bibliometric analysis of 482 papers indexed in Scopus. It also involves the classification and comparison of limbed and limbless animal-inspired robotic systems adapted for movement in soil and sand (locomotion methods such as grabbing-pushing, wriggling, undulating, and rolling) where the most published robots are inspired by worms, moles, snakes, lizards, crabs, and spiders. As a result of this research, this work presents a pioneering methodology for designing bio-inspired robots, justifying the application of biological morphologies for subsurface or surface lunar exploration. By highlighting the technical features of actuators, sensors, and mechanisms, this approach demonstrates the potential for advancing space robotics, by designing biomechatronic systems that mimic animal characteristics.

Patterns of girdle shape and their correlates in Australian limb-reduced skinks

The evolution of limb reduction in squamates is a classic example of convergence, but the skeletal morphological patterns associated with it are underexplored. To provide insights on the biomechanical and developmental consequences of transitions to limb reduction, we use geometric morphometrics to examine the morphology of pectoral and pelvic girdles in 90 species of limb-reduced skinks and their fully limbed relatives. Clavicle shapes converge towards an acute anterior bend when forelimbs are lost but hindlimbs are retained-a morphology typical of sand-swimmers. This may either indicate functional adaptations to locomotion in fine substrates, or a developmental consequence of complete limb loss. The shape of limb-bearing elements of both girdles (coracoid and pelvis) instead closely mirrors limb reduction, becoming more simplified as undulation replaces limbed locomotion. Integration between girdles decreases in taxa lacking elements of the forelimbs but not hindlimbs, indicating differential selection on each girdle in response to distinct locomotory strategies. However, this pattern becomes less clear when considering phylogenetic history, perhaps because it is limited to one specific clade (Lerista). We show how the functional demands of locomotion can induce changes at different levels of organismal organization, including both external and internal structures.

Are toe fringes important for lizard burying in highly mobile sand?

Toe fringes are a key innovation for sand dwelling lizards, and the relationship between toe fringe function and substrate properties is helpful in understanding the adaptation of lizards to sand dune environments. We tested the sand burial performance of Phrynocephalus mystaceus on different sand substrates with toe fringe manipulation, with the aim of assessing whether the function of the toe fringes shifts under different substrate properties, especially in highly mobile substrates. The sand burial performance of P. mystaceus was influenced by substrate properties in relation to the toe fringe states of the lizard. After removal of the bilateral toe fringes, the sand burial ability score of P. mystaceus was significantly higher on sand substrates below 100 mesh than on native sand substrates. As the angle of stability of the substrate properties decreased, the sand burial performance of the lizard was even better after the bilateral toe fringes were removed. The results of the LASSO model and the path analysis model showed that the stability angle provided the opposite effect on sand burial performance in different toe fringe states. These results further suggest that the sand burial function of toe fringes may not be suitable for highly mobile sand substrates. It remains to be tested further whether the function of toe fringes is more important for running on sand.

Geometric phase predicts locomotion performance in undulating living systems across scales

Self-propelling organisms locomote via generation of patterns of self-deformation. Despite the diversity of body plans, internal actuation schemes and environments in limbless vertebrates and invertebrates, such organisms often use similar traveling waves of axial body bending for movement. Delineating how self-deformation parameters lead to locomotor performance (e.g. speed, energy, turning capabilities) remains challenging. We show that a geometric framework, replacing laborious calculation with a diagrammatic scheme, is well-suited to discovery and comparison of effective patterns of wave dynamics in diverse living systems. We focus on a regime of undulatory locomotion, that of highly damped environments, which is applicable not only to small organisms in viscous fluids, but also larger animals in frictional fluids (sand) and on frictional ground. We find that the traveling wave dynamics used by mm-scale nematode worms and cm-scale desert dwelling snakes and lizards can be described by time series of weights associated with two principal modes. The approximately circular closed path trajectories of mode weights in a self-deformation space enclose near-maximal surface integral (geometric phase) for organisms spanning two decades in body length. We hypothesize that such trajectories are targets of control (which we refer to as "serpenoid templates"). Further, the geometric approach reveals how seemingly complex behaviors such as turning in worms and sidewinding snakes can be described as modulations of templates. Thus, the use of differential geometry in the locomotion of living systems generates a common description of locomotion across taxa and provides hypotheses for neuromechanical control schemes at lower levels of organization.

Biomimetic lizard robot for adapting to Martian surface terrain

The exploration of the planet Mars still is a top priority in planetary science. The Mars surface is extensively covered with soil-like material. Current wheeled rovers on Mars have been occasionally experiencing immobilization instances in unexpectedly weak terrains. The development of Mars rovers adaptable to these terrains is instrumental in improving exploration efficiency. Inspired by locomotion of the desert lizard, this paper illustrates a biomimetic quadruped robot with structures of flexible active spine and toes. By accounting for spine lateral flexion and its coordination with four leg movements, three gaits of tripod, trot and turning are designed. The motions corresponding to the three gaits are conceptually and numerically analyzed. On the granular terrains analog to Martian surface, the gasping forces by the active toes are estimated. Then traversing tests for the robot to move on Martian soil surface analog with the three gaits were investigated. Moreover, the traversing characteristics for Martian rocky and slope surface analog are analyzed. Results show that the robot can traverse Martian soil surface analog with maximum forward speed 28.13 m s-1turning speed 1.94° s-1and obstacle height 74.85 mm. The maximum angle for climbing Martian soil slope analog is 28°, corresponding slippery rate 76.8%. It is predicted that this robot can adapt to Martian granular rough terrain with gentle slopes.

Mechanical intelligence simplifies control in terrestrial limbless locomotion

Limbless locomotors, from microscopic worms to macroscopic snakes, traverse complex, heterogeneous natural environments typically using undulatory body wave propagation. Theoretical and robophysical models typically emphasize body kinematics and active neural/electronic control. However, we contend that because such approaches often neglect the role of passive, mechanically controlled processes (those involving "mechanical intelligence"), they fail to reproduce the performance of even the simplest organisms. To uncover principles of how mechanical intelligence aids limbless locomotion in heterogeneous terradynamic regimes, here we conduct a comparative study of locomotion in a model of heterogeneous terrain (lattices of rigid posts). We used a model biological system, the highly studied nematode worm Caenorhabditis elegans, and a robophysical device whose bilateral actuator morphology models that of limbless organisms across scales. The robot's kinematics quantitatively reproduced the performance of the nematodes with purely open-loop control; mechanical intelligence simplified control of obstacle navigation and exploitation by reducing the need for active sensing and feedback. An active behavior observed in C. elegans, undulatory wave reversal upon head collisions, robustified locomotion via exploitation of the systems' mechanical intelligence. Our study provides insights into how neurally simple limbless organisms like nematodes can leverage mechanical intelligence via appropriately tuned bilateral actuation to locomote in complex environments. These principles likely apply to neurally more sophisticated organisms and also provide a design and control paradigm for limbless robots for applications like search and rescue and planetary exploration.

Schrödinger Dynamics and Berry Phase of Undulatory Locomotion

Spectral mode representations play an essential role in various areas of physics, from quantum mechanics to fluid turbulence, but they are not yet extensively used to characterize and describe the behavioral dynamics of living systems. Here, we show that mode-based linear models inferred from experimental live-imaging data can provide an accurate low-dimensional description of undulatory locomotion in worms, centipedes, robots, and snakes. By incorporating physical symmetries and known biological constraints into the dynamical model, we find that the shape dynamics are generically governed by Schrödinger equations in mode space. The eigenstates of the effective biophysical Hamiltonians and their adiabatic variations enable the efficient classification and differentiation of locomotion behaviors in natural, simulated, and robotic organisms using Grassmann distances and Berry phases. While our analysis focuses on a widely studied class of biophysical locomotion phenomena, the underlying approach generalizes to other physical or living systems that permit a mode representation subject to geometric shape constraints.

Multilegged matter transport: A framework for locomotion on noisy landscapes

Whereas the transport of matter by wheeled vehicles or legged robots can be guaranteed in engineered landscapes such as roads or rails, locomotion prediction in complex environments such as collapsed buildings or crop fields remains challenging. Inspired by the principles of information transmission, which allow signals to be reliably transmitted over "noisy" channels, we developed a "matter-transport" framework that demonstrates that noninertial locomotion can be provably generated over noisy rugose landscapes (heterogeneities on the scale of locomotor dimensions). Experiments confirm that sufficient spatial redundancy in the form of serially connected legged robots leads to reliable transport on such terrain without requiring sensing and control. Further analogies from communication theory coupled with advances in gaits (coding) and sensor-based feedback control (error detection and correction) can lead to agile locomotion in complex terradynamic regimes.

Self-propulsion via slipping: Frictional swimming in multilegged locomotors

Locomotion is typically studied either in continuous media where bodies and legs experience forces generated by the flowing medium or on solid substrates dominated by friction. In the former, centralized whole-body coordination is believed to facilitate appropriate slipping through the medium for propulsion. In the latter, slip is often assumed minimal and thus avoided via decentralized control schemes. We find in laboratory experiments that terrestrial locomotion of a meter-scale multisegmented/legged robophysical model resembles undulatory fluid swimming. Experiments varying waves of leg stepping and body bending reveal how these parameters result in effective terrestrial locomotion despite seemingly ineffective isotropic frictional contacts. Dissipation dominates over inertial effects in this macroscopic-scaled regime, resulting in essentially geometric locomotion on land akin to microscopic-scale swimming in fluids. Theoretical analysis demonstrates that the high-dimensional multisegmented/legged dynamics can be simplified to a centralized low-dimensional model, which reveals an effective resistive force theory with an acquired viscous drag anisotropy. We extend our low-dimensional, geometric analysis to illustrate how body undulation can aid performance in non-flat obstacle-rich terrains and also use the scheme to quantitatively model how body undulation affects performance of biological centipede locomotion (the desert centipede Scolopendra polymorpha) moving at relatively high speeds (∼0.5 body lengths/sec). Our results could facilitate control of multilegged robots in complex terradynamic scenarios.

Walking is like slithering: A unifying, data-driven view of locomotion

Legged movement is ubiquitous in nature and of increasing interest for robotics. Most legged animals routinely encounter foot slipping, yet detailed modeling of multiple contacts with slipping exceeds current simulation capacity. Here we present a principle that unifies multilegged walking (including that involving slipping) with slithering and Stokesian (low Reynolds number) swimming. We generated data-driven principally kinematic models of locomotion for walking in low-slip animals (Argentine ant, 4.7% slip ratio of slipping to total motion) and for high-slip robotic systems (BigANT hexapod, slip ratio 12 to 22%; Multipod robots ranging from 6 to 12 legs, slip ratio 40 to 100%). We found that principally kinematic models could explain much of the variability in body velocity and turning rate using body shape and could predict walking behaviors outside the training data. Most remarkably, walking was principally kinematic irrespective of leg number, foot slipping, and turning rate. We find that grounded walking, with or without slipping, is governed by principally kinematic equations of motion, functionally similar to frictional swimming and slithering. Geometric mechanics thus leads to a unified model for swimming, slithering, and walking. Such commonality may shed light on the evolutionary origins of animal locomotion control and offer new approaches for robotic locomotion and motion planning.